Practice problems for exam 2. - John Fricks

Stat 416, Practice Problems
1. Customers arrive at a shipping office at times of a Poisson process with
rate 3 per hour. The office was supposed to open at 8 AM but the
clerk Oscar overslept and came in at 10 AM.
(a) What is the probability that no customer came in the two hours
before Oscar arrived?
(b) If one customer did arrive between 8 and 10, what is the expected
value of his wait for Oscar?
(c) If no customer arrived before 10, what is the distribution of the
time that Oscar must wait for the arrival of the first customer?
(d) What is the variance of the time until the fifth customer arrives
after 10 AM?
2. Traffic on a particular road follows a Poisson process with rate 6 cars
per minute. A deer runs out of the woods, and it takes the deer 5
seconds to cross the road.
(a) What is the probability the deer will get hit?
(b) If the deer can cross in two seconds, what is the probability the
deer will get hit?
(c) If a car passes some time in the 10 seconds after the deer starts
across the road and it takes the deer 5 seconds to get across, what
is the probability that the deer will be hit?
3. Suppose that the number of calls per hour to an answering service
follows a Poisson process with rate 4.
(a) What is the probability that fewer than two calls came in the
first hour?
(b) Suppose that six calls arrive in the first two hours, what is the
probability exactly two arrived in the first hour and four in the
second hour.
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(c) Suppose that the operator gets to take a break after she has answered
ten calls. How long are her average work periods?
Now, suppose that 3/4 of the calls are made by men and 1/4 by
women.
(d) Given that 3 men call in one hour, what is the probability that 2
women call in that hour?
(e) What is the probability that in one hour exactly 2 men and 3
women will call the answering service?
(f) What is the average time before 3 women call?
4. Edwin catches fish at time that correspond to a Poisson process with
rate 3 per hour. Suppose 40% of the fish are salmon and 60% are trout.
The trout weigh an average of 4 pounds with a standard deviation of
2 pounds. Find the mean and standard deviation of the total weight
of trout he catches in two hours.
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